Currently, the electric automatic-drip coffee maker with grinder is quite popular for its convenience and practicability in use. However, how to reduce the time interval during which the coffee grounds are exposed in air, how to reduce the heat consumed in coffee making, and how to completely prevent the water steam from entering the grinder through the coffee grounds discharge passage are always big concerns for people. U.S. Pat. No. 5,615,601 disclosed a coffee machine with a coffee grinder defining a grinding position there under. Said grinding position is horizontally spaced from the brewing position. There is also provided a filter carrier adapted to receive a filter basket, and a displacing mechanism for supporting the filter carrier and for moving the filter carrier into the grinding position or into the brewing position. In use, since the filter basket is required to be displaced frequently, the lifetime of the whole coffee machine is affected.